Problem 6.2.3 (adapted from an earlier demo for 6.2.2)
Here are the pictures  I tried to draw on the board.

First, the two-dimensional region. (Ignore all the technical stuff; just look at the pictures!) The red rectangle will be the base of the "square" perpendicular to the x-axis.

Let's isolate the region a bit better. (Note that the axes no longer cross at the origin.)

Here is a 3-D view of the square cross-section.

Here's a bunch of 'em, along with the red one.